Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch square pan.
In a large mixing bowl, beat eggs for 4 minutes with electric mixer. Gradually add sugar; beat until light and fluffy, 4 to 5 minutes.
Whisk together the flour and baking powder, and add to egg mixture until just combined.
In a saucepan, heat 1/2 cup milk and 2 tablespoons butter until butter is melted. Gradually pour into the batter, mixing constantly. Pour into prepared pan.
Bake in preheated oven until cake is golden and a toothpick inserted in the center of the cake comes out clean, 20 to 25 minutes.
Remove cake from oven; preheat oven’s broiler.
Beat 1/4 cup brown sugar and 2 tablespoons butter until combined. Stir in milk to desired consistency. Stir in coconut and nuts. Spread over warm cake. Broil 4 inches from heat for 3 to 4 minutes, till golden.